Suppose I have a matrix that looks like this
[,1] [,2]
[1,] 2.415212e-09 9.748863e-10
[2,] -2.415212e-09 5.029136e-10
How do I make it positive definite? I am not looking for specific numerical value answer, but a general approach to this problem.
I have heard...
Hi, all
I have been reading about copula, but still very confused.
What exactly is a copula? My understanding is: there are couple of components
1. uniform cdf marginal
2. a covariance matrix
What exactly is this thing? Why am I calculating the marginals and what does it have to do...
Homework Statement
How do you integrate this?
x-ae-b/x, where a and b are some constants.
The Attempt at a Solution
I have tried this
http://integrals.wolfram.com/index.jsp?expr=x+*+e^%28-1%2Fx%29&random=false
Is there a closed form of this?
What test or distribution should I use for before and after treatment?
Say, I have 30 subjects I test their blood before and after a pill they take a pill, what kind of test should I use?
I want to test mean difference, so, paired t-test? or Wilcoxon signed rank test?
The data looks like this...
Homework Statement
Want to prove that [0,1] in R is compact. Let \bigcup_{\alpha\in A} I_{\alpha} be an open cover of [0,1].
By open sets in R.
Let E={t\in[0,1] s.t. [0,t] is covered by a finite number of the open cover sets I_{\alpha}}.
Prove that E\neq\emptyset.
The Attempt at a...
Homework Statement
Are interior points included in (or part of) limit points?
Homework Equations
Since the definition of interior points says that you can find a ball completely contained in the set. For limit points, it's less strict, you just have to find a point other than the center...
I was wondering how to prove rational number is a commutative field.
Personally, I didn't think the word "commutative" is necessary, how about others?
Do I simply prove it is commutative under multiplication?
In an ANOVA experiment, you have,
group mean \overline{y}.
overall mean \overline{y}..
Are they independent?
Some samples overlap to calculate these means.
What is var(\overline{y}.-\overline{y}..) ?
Homework Statement
Let X and Y be two unknown variables with E(Y)=\mu and EY2 < \infty.
Homework Equations
a. Show that the constant c that minimizes E(Y-c)2 is c=\mu.
b. Deduce that the random variable f(X) that minimizes E[(Y-f(X))2|X] is f(X)= E[Y|X].
c. Deduce that the random variable...
I am learning Stochastic Processes right now. Can someone some explain why waiting time is memoryless? Say, if a light bulb has been on for 10 hours, the probability that it will be on for another 5 is the same as the 1st 5 hours.
It doesn't make sense to me, because the longer you use it...